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arXiv · 0812.5055

Schrödinger and related equations as Hamiltonian systems, manifolds of second-order tensors and new ideas of nonlinearity in quantum mechanics

J. J. Sławianowski·V. Kovalchuk
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Abstract

Considered is the Schrödinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting example of "mechanics" with singular Lagrangians, effectively treatable within the framework of Dirac formalism. We discuss also some modified "Schrödinger" equations involving second-order time derivatives and introduce a kind of non-direct, non-perturbative, geometrically-motivated nonlinearity based on making the scalar product a dynamical quantity. There are some reasons to expect that this might be a new way of describing open dynamical systems and explaining some quantum "paradoxes".

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J. J. Sławianowski, V. Kovalchuk. 2009-11-18. Schrödinger and related equations as Hamiltonian systems, manifolds of second-order tensors and new ideas of nonlinearity in quantum mechanics. https://arxiv.org/abs/0812.5055

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